a:b = c:d → a×d = b×c [Cross-product]

↳3:4 = x:20 → x = 15 (cross-multiply 3×20 = 4x)

Mean Proportional : x = √(a×c)

↳between 4 and 9 → √(4×9) = 6

Fourth Proportional: x = (b×c) ÷ a

↳a=2, b=4, c=10 → x = (4×10)/2 = 20

Direct Variation : y = kx (y∝x)

↳y = 3x → if x doubles, y doubles

Inverse Variation : y = k/x (y∝1/x)

↳y = 24/x → x=4 gives y=6, x=12 gives y=2

Compound Ratio : (a:b) × (c:d) = ac:bd

↳(2:3) × (5:4) = 10:12 = 5:6